The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  1  1 X^2+X  1 X^2 X^2 X^2  1
 0  1  0  0  1 X^2+X+1  1 X^2  1 X+1  X  X X^2+X  1  1  1 X^2
 0  0  1  1  1  0  1 X^2+X X+1 X^2+X X+1  1 X^2+X+1 X^2  0 X^2+1  0
 0  0  0  X X^2 X^2+X X^2+X X^2+X X^2+X X^2  X  X X^2  X X^2 X^2+X X^2+X

generates a code of length 17 over Z2[X]/(X^3) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+44x^13+199x^14+286x^15+307x^16+384x^17+350x^18+252x^19+132x^20+52x^21+35x^22+6x^23

The gray image is a linear code over GF(2) with n=68, k=11 and d=26.
This code was found by Heurico 1.16 in 0.0293 seconds.